Problem: Simplify the following expression: $ z = \dfrac{-7x + 2}{10} - \dfrac{-6}{5} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-7x + 2}{10} \times \dfrac{5}{5} = \dfrac{-35x + 10}{50} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-6}{5} \times \dfrac{10}{10} = \dfrac{-60}{50} $ Therefore $ z = \dfrac{-35x + 10}{50} - \dfrac{-60}{50} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-35x + 10 + 60 }{50} $ Distribute the negative sign: $z = \dfrac{-35x + 10 + 60}{50}$ $z = \dfrac{-35x + 70}{50}$ Simplify the expression by dividing the numerator and denominator by 5: $z = \dfrac{-7x + 14}{10}$